Damage detection in beams using time-frequency analysis of transient flexural waves

In this paper, a methodology for locating and determining the size of transverse open cracks in beams based on time-frequency analysis of transient flexural waves is presented. A beam with a transverse open crack modeled as a rotational spring is considered. The wave field along the beam generated by an impact force is calculated and expressions for the reflection coefficients as a function of frequency and crack depth are derived. Simulated signals for the acceleration response of the beam for different crack depths are calculated and further analysed employing time-frequency analysis to extract the dispersive characteristics. The location of the crack is estimated using the arrival time of reflected waves. The ratio of the reflected wave energy to the incident wave energy is calculated and used as an indicator of crack size. The estimated reflection coefficients from the simulated signals are in excellent agreement with theory. To validate the theoretical predictions, a series of experiments on a cracked brass beam were carried out. The measured signals were analysed and both the location and size of the crack were estimated. The experimental results verify the effectiveness of the proposed methodology.